How can I rig a multiple-axis robot?
Is there any Blender function that supports the above movement?


You are looking for solving the motion with Inverse Kinematics, in fact exactly like an industrial robot solves joint trajectories needed for the robot to guide some tool along some trajectory.

Here is the documentation.

You put IK constraint(s) on last bone of bone chain(s) you want to control to comply with some given position/motion given by another object or bone (the target for the solver).

For every bone of this chain you can also limit the degrees of motion for each joint. The settings are under Bone tab in Properties panel.